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\def\be{\begin{equation}}
\def\ee{\end{equation}}
\def\indigo{{\em IndIGO }}
\def\msun{$M_\odot$}
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\begin{document}
\title{Astrophysical implications of a GW detector network (in particular \indigo)}

\author{{\Large INTERNAL DRAFT...NOT FOR CIRCULATION}}

\date{\today}
\maketitle
\large 
\section{Sky coverage for compact binary sources}
 Examine the sky coverages of a GW network including {\em IndIGO}.
%\subsubsection{Binary NS detectability}
\begin{enumerate}
\item \underline{\bf Binary NS}: Distribute $10^4$ BNS sources randomly in the sky (random $\theta,\phi,\psi,\iota$) within a redshift of 0.25 (this is $\sim 1.1 Gpc$) and compute the network SNR for each one and plot the detectable (SNR greater than a threshold ($\rho=8$?)) binaries in the $\theta-\phi$ plane. Compare
this plot for  LHVA, LHVI and LHVAI configurations.

%\subsubsection{NS-BH systems}
\item \underline{\bf NS-BH}: Same exercise but now NS of 1.4\msun and BH of 10\msun distributed uniformly up to $z=0.5$ (roughly 3Gpc)

\item \underline{\bf Binary BHs}: Distribute BBH (of various masses, but which range??)
up to $z=1$ and repeat the same.\\
\comment{Arun: A similar analysis was done in Ref.~\cite{Nissanke09a}. They find that inclusion of AIGO and LCGT makes the sky coverage almost uniform. Instead of LCGT we have \indigo here. Since this involves only SNR calculation, it will be a good warm up.}
\end{enumerate}
\section{BNS and NS-BH cases associated with a ShGRB observation}
This is something we should carefully explore, given that \indigo may
be projected as a high frequency advanced detector.  The usual things to look at are
\begin{enumerate}
\item Given the source position  and redshift is known exactly from ShGRB observation, what are the typical luminosity distance errors a GW network can provide.
Redshift determination from optical afterglow for {\it long} GRBs is routine. But due to the short duration signals of ShGRBs, it is not clear how well can the position and redshift be estimated from EM observations. I think many of the redshift estimates for ShGRBs have come from indirect methods. \\\ttd{ Arun will look up the GRB literature and see what are the typical localization errors for ShGRBs and methods for estimtion of redshifts. Also try to see what are the projected accuracies for them with the future EM instruments by the time of Adv LIGO. }
See some recent reviews in Refs.~\cite{BloomDeccadal09,PhinneyDeccadal09}.
\item In the parameter estimation of BNS and NS-BH systems, see the effect of
higher harmonics.
\item Use Gaussian priors on almost ALL parameters to get the best estimates.
It also helps to reduce the possible ill-conditionedness of the Fisher matrix.
\item We should also look at the typical values of `polarization resolution'~\cite{Jennrich97} the solid angle subtended by $\iota-\psi$ angles.
\end{enumerate}
\section{BNS, NS-BH and BBH cases with no EM afterglow: using galaxy catalogs}
\begin{enumerate}
\item Angular resolutions for BNS and NS-BH--HHs improve angular resolution?--
can low z catalogs (such as SDSS) be used to identify the host galaxy cluster associated with these events?
\item Another possibility is that followed by the GW detection and localization,
one can launch a multiwavelength EM follow up in that patch of the sky. This
will be useful if the source coordinates do not coincide with any survey.
Such a follow up, together with the distance estimation from GW observations
{\it could} help to find association of GW event with a  even
a galactic cluster or a galaxy if we are lucky.

Fro the GRB literature, typical angular diameter of the source for association with a galactic cluster
is less than 10'(note that 0.01 sq deg resolution will correspond to 6')
and 10" for a galaxy association~\cite{BergerShGRBCluster07}. But given the independent distance estimation
GW observations have, it could be relaxed, I think.

Ref~\cite{BergerShGRBCluster07}, for example, discusses a series of follow ups
to find any association of GRBs (whose redshifts are known from optical afterglows) with a galactic clusters. The motivation for these is to study the typical
galactic environment which gives rise to ShGRBs and see if there is any systematic trends (such as the hypothesis that ShGRBs are from old evolved galaxies if compact binary progenitors). From a GW perspective, though our first aim may be
to obtain a redshift via galaxy association, the above mentioned astrophysics
will also be interesting to probe (But its difficult to forecast anything about them because these can only be done after a sure shot detection) such as an EM follow up of a patch of the sky where a BBH merger was observed!!
\ttd{Arun will look into some of these possibilities (EM follow up using Indian telescopes such as Nainital optical telescope, IUCAA optical, GMRT, Astrosat(?))
in the \indigo context.}
Question: In the case of shGRBs what is the typical time between merger
and afterglow?
\end{enumerate}
\appendix
\section{Typical GCN about ShGRB's Galactic Cluster association}
{\tt TITLE:   GCN GRB OBSERVATION REPORT\\
NUMBER:  3962\\
SUBJECT: GRB 050911: z$\simeq$0.16 cluster in the field\\
DATE:    05/09/11 16:50:31 GMT\\
FROM:    Edo Berger at Carnegie Obs  <eberger@ociw.edu>\\

E. Berger (Carnegie Observatories) reports:\\

"The position of GRB 050911 is located about 3.5 arcmin from the center of
a galaxy cluster (EDCC 493; diameter ~ 20 arcmin).  Several galaxies in
this field have a redshift of about 0.165, measured in the {\bf Las Campanas
Redshift Survey (LCRS)}.  If GRB 050911 is a short burst (as may be
indicated by the initial short duration pulses; GCN 3961), then it is
possible that it is associated with EDCC 493, and is therefore located at
z~0.16.  We note that the prompt emission exhibits a second peak at t+10
to t+20 sec (GCN 3961), but this may be a softer component as observed in
GRBs 050709 and 050724."
}
\bibliography{indigo-ref}
\end{document}
